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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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1435-5337
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Volume 28, Issue 2

Issues

Specifying the Auslander–Reiten translation for complexes of modules

Shokrollah Salarian
  • Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran; and School of Mathematics, Institute for Research in Fundamental Science (IPM), P.O. Box 19395-5746, Tehran, Iran
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/ Razieh Vahed
  • Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran; and School of Mathematics, Institute for Research in Fundamental Science (IPM), P.O. Box 19395-5746, Tehran, Iran
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Published Online: 2015-01-10 | DOI: https://doi.org/10.1515/forum-2013-0209

Abstract

We describe explicitly the Auslander–Reiten translation in the category of bounded complexes of finitely generated maximal Cohen–Macaulay modules, 𝐂b(CM R), over a commutative local Cohen–Macaulay ring R with a canonical module ω. Then the Auslander–Reiten formula is generalized for complexes in 𝐂b(CM R) and we prove the existence theorem of Auslander–Reiten sequences. As an application of our results, we investigate the existence of Auslander–Reiten triangles in the category of perfect complexes as a full triangulated subcategory of 𝐃b(mod R).

Keywords: Auslander–Reiten sequences; maximal Cohen–Macaulay modules; adjoin pair; homotopy category

MSC: 18G35; 18E30; 16G50; 16G70

About the article

Received: 2013-12-29

Revised: 2014-08-03

Published Online: 2015-01-10

Published in Print: 2016-03-01


Funding Source: IPM

Award identifier / Grant number: 92130218


Citation Information: Forum Mathematicum, Volume 28, Issue 2, Pages 377–389, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-0209.

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